On the dimension of affine subspaces of nilpotent matrices
arXiv:2508.06653 · doi:10.1016/j.laa.2026.08.015
Abstract
The focus of the paper is on the maximal dimension of affine subspaces of nilpotent n x n matrices with fixed rank. In particular we obtain a result in the "border" case rank equal to n-1; we also consider the much simpler case rank equal to 1.